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JEE Main202622 January 2026Evening ShiftMathematicsVector AlgebraActual

Let a =2 i - j + k and b = j +2 k , Z be two vectors. Let c = a b and d be a vector of magnitude 2 in y z -plane. If | c |= 53 , then the maximum possible value of ( c d )² is equal to :

Options

  1. A26
  2. B52
  3. C208
  4. D104

Correct answer

C. 208

Step-by-step solution

a = 2 i - j + k b = j + 2 k ; Z c = a b = (-2 - ) i - 4 j + 2 k | c | = 53 5 ^2 + 4 - 33 = 0 = 2.2 or -3 = -3 c = i - 4 j - 6 k let d = y j + z k | d | = 2 y^2 + z^2 = 4 ( c d )^2 = (4y + 6z)^2 ( 4^2 + 6^2 y^2 + z^2 )^2 208

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